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# Algebra

1. The equation D=1.2&#8730;h gives the distance, D, in miles that a person can see to the horizon from a height, h, in feet. a. Solve this equation for h. b. Long's Peak in the Rocky Mountain National Park, is 14,255 feet in elevation. How far can you see to the horizon from the top of Long's Peak? Can you see Cheyenne

### Solving Radical Equations and Word Problems

See the attachment. 1. Solve the equation for r. 2. Suppose that an object is 100 pounds when it is at sea level. Find the value of C that makes the equation true. (Sea level is 3,963 miles from the center of the earth.) 3. Use the value of C you found in the previous question to determine how much the object would wei

### The Period of a Pendulum

The period T (time in seconds for one complete cycle) of a simple pendulum is related to the length L (in feet) of the pendulum by the formula 8T^2=(3.14)^2L. If a child is on a swing with a 10 foot chain, then how long does it take to complete one cycle of the swing?

### Solve and Graph a Rational Inequalities

I am terrible at graphing and I need to solve the rational inequality. I need to state and graph the solution set. a/a+2 >0

### Solve an Integer Program Problem: Optimal Solution

Max Z = 5x1 + 6x2 Subject to: 17x1 + 8x2 <= 136 3x1 + 4x2 <= 36 x1, x2 >= 0 and integer What is the optimal solution? Z = ? Put your answer in the form xx with no additional numbers or symbols.

### Integer Linear Programming and Optimal Solution

1. Consider the following integer linear programming problem. Max Z = 3x1 + 2x2 Subject to: 3x1 + 5x2 <= 30 4x1 + 2x2 <= 28 x1 <= 8 x1, x2 >= 0 and integer The solution to the linear programming relaxation is: x1 = 5.714, x2= 2.571. What is the optimal solution to the integer linear programming problem? State the value

### Linear Programming

Consider the following linear programming problem Max 8X + 7Y s.t. 15X + 5Y < 75 10X + 6Y < 60 X + Y < 8

### Demand and Revune Equations for the Sale of Tiles

A. Suppose that a market research company finds that at a price of p = \$20, they would sell x = 42 tiles each month. If they lower the price to p = \$10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month's time. Find the equation of the line for the demand equation. Write your answer in

### Writing Inequalities from Word Problems

Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost \$60 and each tree is \$84, what is the maximum number of trees you can buy with a budget for rock and trees of \$2500? Write an inequality that illustrat

### Demand Equations

Suppose that a market research company finds that at a price of p = \$20, they would sell x = 42 tiles each month. If they lower the price to p = \$10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month's time. Find the equation of the line for the demand equation. Write your answer in th

### Linear Programming

Consider the following linear programming problem. MIN Z = 10x1 + 20x2 Subject to: x1 + x2 >= 12 2x1 + 5x2 >= 40 x1, x2 >= 0 What is minimum cost Z=?? Put your answer in the xxx.x (to one decimal place)

### Prove that W is a Subspace of V

Let F be the field of real numbers and let V be the set of all sequences: (a_1, a_2, ..., a_n, ...), a_i belongs to F, where equality, addition and scalar multiplication are defined component wise. Then V is a vector space over F. Let W = {(a_1, a_2, ..., a_n, ...) belongs to V | lim n -> infinity a_n = 0}. Prove t

### Writing an equation in standard form (only integers)

What process should I follow to write an equation in standard form if at the end the equation has a zero? For example: 5x/3 + 6= 0

### CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest.

CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Crane came out and gratefully thanked the traveling salesman for saving his daughter's life. Mr. Crane

### Use the geometric sequence of numbers 1, 3, 9, 27, ... to find the following

A) What is r, the ratio between 2 consecutive terms? b) Using the formula for the nth term of a geometric sequence, what is the 10th term? c) Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms?

### Arithmetic and Geometric Series and Sequences

Using the index "n" of the partial sums of a series as the domain, and the value of the corresponding partial sums of the series "Sn" as the range, is a series a function? Please include in your answer: - Which of the basic functions, (i.e. - linear, quadratic, rational, exponential), is related to the arithmetic series? -

### Arithmetic and Geometric Sequences and Series

Please provide some guidance and references to develop the homework. Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any two consecutive terms? Answer: Show work in this space. b) Using the formula for the nth term of an arithmetic sequence,

### Fibonacci Series

What is the connection between rabbit farming, sun-flowers and pine cones? Hint: It's related to "Fibonacci Series."

### 'Together and Alone' Word Problems

Winston can mow his dad's lawn in 1 hour less than it takes his brother Willie. If they take 2 hours to mow it when working together, then how long would it take Winston working alone? I know that I need to use a quadratic equations but I'm lost on which way to set it up?

### Solving equations, difference between relation and function

Please see the attached file for full description Find all real or imaginary solutions to each equation: 98. X - 1 = 2x - 3 X + 2 x + 4 Find exact and approximate solutions to each problem 106. One on one. Find two positive real numbers that differ by 1 and have a product of 1. 115. Decathlon champion. For

### Linear Programming: Maximization and Transportation

39. Max Z = \$0.30x + \$0.90y Subject to : 2x + 3.2y <= 160 4x + 2y <= 240 y <= 40 x, y >= 0. Solve for the quantities of x and y which will maximize Z. What is the value of the slack variable associated with constraint 2? 45. Consider the following transportation problem: 1 2 Supply 1 5 6 100

### Writing Equations from Word Problems

12) You have exactly \$537 to spend on parting gifts for your rich uncle's birthday party. You decide to get watches for the ladies (at \$27.98 each), and beepers for the men (at \$23.46 each). You know that the number of watches required will be 3 times as much as the number of beepers. How many of each item do you buy?

### Linear Relationships, Slope and Intercept

1. The following data shows the relationship between the total average amount of student study time in an Online course and their corresponding average grades. Hours Studied 50 57 69 112 120 88 96 Grade 60 63.5 69.5 91 95 79 83 Is this relationship linear? Explain why or why not 2. Line 1 passes through the points

### Small Stage Efficiency of a Gas Turbine and Rearranging Equations

6. The overall efficiency of a gas turbine can be calculated from the formula ..... where is the small stage efficiency and E =..., where r is the expansion pressure ratio and gamma is the ratio of the specific heats. Given that the overall efficiency nf is 76%, r = 4.6 and that y = 1.333, calculate the value of the small sta

### Loudness of Sound

The loudness of sound is based on intensity level measured in decibels using a logarithmic scale and is relative to (a ratio of) the weakest sound the ear can hear. Research how sound is measured. Include the following items in your posting: The formula for measuring sound. Pick a specific sound, give the decibels of

### Discriminants

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx +

### Discriminants

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx +

### Fitting an ellipse using least squares.

Can the method attached be adapted for an an ellipse rotated and not centered at the origin? Please explain. keywords: ellipse-fitting

### Continuously Compounding Interest..

1. A woman deposits \$50,000 in a savings account with 4% continuously compounded interest. How many years must she wait until the balance has doubled? Use the Compounding continuously formula and show the steps involved in getting the solution. 2. True or false: The function " f(x) = 3^x " grows three times faster than the fu

### Annihilators and Ideals

Let R be a commutative ring and let A be any subset of R. The annihilator of A, denoted by Ann(A), is the set {r in R:r(a)=0 for all a in A}. Show that Ann(A) is an ideal of R. See attached file for full problem description.